Tuesday, August 9, 2011

Empirical Formula for #Days Between V. Equinox & A. Equinox

I used different values for the eccentricity of the Earth's orbit, e, to get a set of values for the coefficients of the formula found last time. A turned out to be a constant equal to half the number of days in the year and B was a simple function of e. θ is the angle of Earth's perihelion from the direction of the Winter Solstice in the Earth's orbital plane or 90° behind the Vernal Equinox.

I labeled the function for the number of days from the Vernal Equinox to the Autumnal Equinox VEq2AEq. The empirical error bound is a simple cubic function within the range of e for the formula, 0 < e < 0.07.

Supplemental (Aug 10): The polynomial fit for B(e) had some near zero values so I tried doing a least squares fit for just odd powers of e and got a better fit.
The rms error was 2·10-10. The function appears to be,
   B(e) = 232.520·(e - e3/3! - 3e5/5! + ···).

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